The present invention pertains generally to devices and methods for separating charged particles in a plasma according to their respective masses. More particularly, the present invention pertains to devices for placing low-mass and high-mass particles on different, predictable trajectories to thereby separate the particles according to their respective masses. The present invention is particularly, but not exclusively, useful as a filter to separate high-mass particles from low-mass particles.
There are many reasons why it may be desirable to separate or segregate mixed materials from each other. One such application where it may be desirable to separate mixed materials is in the treatment and disposal of hazardous waste. For example, it is well known that of the entire volume of nuclear waste, only a small amount of the waste consists of radionuclides that cause the waste to be radioactive. Thus, if the radionuclides can somehow be segregated from the non-radioactive ingredients of the nuclear waste, the handling and disposal of the radioactive components can be greatly simplified and the associated costs reduced.
Indeed, many different types of devices, which rely on different physical phenomena, have been proposed to separate mixed materials. For example, settling tanks which rely on gravitational forces to remove suspended particles from a solution and thereby segregate the particles are well known and are commonly used in many applications. As another example, centrifuges which rely on centrifugal forces to separate substances of different densities are also well known and widely used. In addition to these more commonly known methods and devices for separating materials from each other, there are also devices which are specifically designed to handle special materials. A plasma centrifuge is an example of such a device.
As is well known, a plasma centrifuge is a device which generates centrifugal forces to separate charged particles in a plasma from each other. For its operation, a plasma centrifuge necessarily establishes a rotational motion for the plasma about a central axis. A plasma centrifuge also relies on the fact that charged particles (ions) in the plasma will collide with each other during this rotation. The result of these collisions is that the relatively high-mass ions in the plasma will tend to collect at the periphery of the centrifuge. On the other hand, these collisions will generally exclude the lower mass ions from the peripheral area of the centrifuge. The consequent separation of high-mass ions from the relatively lower mass ions during the operation of a plasma centrifuge, however, may not be as complete as is operationally desired, or required.
Apart from a centrifuge operation, it is well known that the orbital motions of charged particles (ions) which have the same velocity in a magnetic field, or in crossed electric and magnetic fields, will differ from each other according to their respective masses. Thus, when the probability of ion collision is significantly reduced, the possibility for improved separation of the particles due to their orbital mechanics is increased. For example, U.S. Pat. No. 6,096,220, which issued on Aug. 1, 2000 to Ohkawa, for an invention entitled xe2x80x9cPlasma Mass Filterxe2x80x9d and which is assigned to the same assignee as the present invention, discloses a device which relies on the different, predictable, orbital motions of charged particles in crossed electric and magnetic fields to separate the charged particles from each other. In the filter disclosed in Ohkawa ""220, the magnetic field is oriented axially, the electric field is oriented radially, and both the magnetic field and the electric field are substantially uniform both azimuthally and axially. As further disclosed in Ohkawa ""220, this configuration of fields causes ions having relatively small mass to charge ratios to be confined inside the chamber during their transit of the chamber. On the other hand, ions having relatively large mass to charge ratios are not so confined. Instead, these larger mass ions are collected inside the chamber before completing their transit through the chamber.
Expanding on the general principles previously disclosed in the Ohkawa ""220 patent for separating ions of different mass, the present invention has recognized that by appropriately modifying the electric and magnetic fields in the filter chamber, the effective magnetic field strength can be reduced. Further, a unidirectional axial velocity can be imparted on the particles, helping the light mass particles transit through the chamber, and preventing buildup of waste on the injection end plate. Specifically, the filter concept disclosed in the Ohkawa ""220 patent can be generalized to the case where the fields are helically symmetric. More specifically, helical symmetry includes the case of azimuthally symmetric but axially bumpy fields as a special case.
Consider the Hamiltonian, H of a charged particle in the magnetic and electric fields.
H=pr2/2M+[pxcex8xe2x88x92erAxcex8]2/[2Mr2]+[pzxe2x88x92eAz]2/[2M]+e"PHgr"xe2x80x83xe2x80x83[1]
where p is the canonical momentum, M is the mass, A is the vector potential, "PHgr" is the electrostatic potential, and e is the charge. In the helically symmetric configurations, both the vector potential and the electrostatic potential are functions of xcfx86 defined by
xcfx86=mxcex8+kz.xe2x80x83xe2x80x83[2]
where xcex8 is the angle around the cylindrical axis and m is the azimuthal mode number, while z is the coordinate along the cylinder and k is the axial mode number.
From the Hamiltonian, the following expression can be obtained
d/dt[kpxcex8xe2x88x92mpz]=0.xe2x80x83xe2x80x83[3]
Thus, the helical canonical momentum ph=k pxcex8xe2x88x92m pz is a constant of motion.
A new Hamiltonian, K can be defined by
K=H+uphxe2x80x83xe2x80x83[4]
where u is a constant having the dimensions of the velocity. The expression
K=pr2/2M+[pxcex8+ukMr2xe2x88x92erAxcex8]2 /[2Mr2]+[pzxe2x88x92umMxe2x88x92eAz]2+Uxe2x80x83xe2x80x83[5]
follows, where
xe2x80x83U=xe2x88x92Mu2[m2+k2r2]/2xe2x88x92eu"psgr"h+e"PHgr"xe2x80x83xe2x80x83[6]
and
"psgr"h=mAzxe2x88x92krAxcex8xe2x80x83xe2x80x83[7]
The helical flux function "psgr"h defines the flux surface.
The second and the third terms represent the kinetic energy in the coordinates that rotates at the angular frequency, xe2x88x92ku and travels in the axial direction at the velocity, mu. The potential, U determines the orbit confining properties. The first term in U is the centrifugal term, the second term is the magnetic confinement term and the last term is the electrostatic driving term. It has the form similar to the filter disclosed in the Ohkawa ""220 patent. The difference is that the vector potential of the uniform magnetic field is replaced by the helical flux function.
The magnetic field with uniform axial magnetic field, B0 superposed with the field from the helical windings is given by
Br=xe2x88x92ibImxe2x80x2[kr]exp[imxcex8+ikz]
Bxcex8=[b/kr]Imexp[imxcex8+ikz]xe2x80x83xe2x80x83[8]
Bz=bImexp[imxcex8+ikz]+B0
where Im is the modified Bessel function, the prime denotes the derivative and b represents the strength of the helical field. B0 is chosen to be larger than b.
The helical flux function is given by
"psgr"h=xe2x88x92[k r2/2]B0xe2x88x92brImxe2x80x2[kr]exp[imxcex8+ikz]xe2x80x83xe2x80x83[9]
Among the choices of m number, only m=0 and m=2 have r2 dependence near the axis. As far as the cut-off mass is concerned, the conditions are identical for m=2 and m=0. Thus
"psgr"h=xe2x88x92[kr2/2][B0+b cos[2xcex8+kz]]xe2x80x83xe2x80x83[10]
and putting
"PHgr"=[xcex1/k]"psgr"hxe2x80x83xe2x80x83[11]
the expression
U=xe2x88x92[Mr2/2]{k2u2xe2x88x92[kuxe2x88x92xcex1][xcexa90+xcexa9h cos[2xcex8+kz]]}xe2x80x83xe2x80x83[12]
can be obtained, where xcexa90=eB0/M and xcexa9h=eb/M.
The constant U surface, namely the guiding center surface, is either an ellipse or a hyperbola. The cut-off mass is defined as the mass above which the constant U surface becomes a hyperbola. The condition is given by
xcex1 greater than [xcexa90xe2x88x92xcexa9h]/4xe2x80x83xe2x80x83[13]
The difference from the filter disclosed in the Ohkawa ""220 patent is that the helical field reduces the effective magnetic field strength. Also, the plasma not only rotates, but also has a unidirectional axial velocity resulting from the radial electric field crossed with the xe2x80x9cthetaxe2x80x9d component of b. The cut-off mass, Mc is given by the weakest field of the bumpy field.
Since the magnetic field is non-uniform, there may be the mirror trapped ions. However the constant U surface opens up at the weakest magnetic field and the mirror trapped ions with the mass above cut-off will go out radially.
In the collisional regime, the thermal equilibrium distribution of an ensemble of ions is proportional to exp[xe2x88x92K/xcexaT]. Only the ions with the mass below cut-off will be confined in a finite volume.
In light of the above, it is an object of the present invention to provide a plasma mass filter which has azimuthally symmetric but axially bumpy fields. Another object of the present invention is to provide a plasma mass filter that is operable at a relatively low effective magnetic field strength. Still another object of the present invention is to provide a plasma mass filter which imparts a uni-directional axial velocity on the particles, helping the light mass particles transit through the chamber and reducing buildup on the injection end plate. Yet another object of the present invention is to provide a Helically Symmetric Plasma Mass Filter which is easy to use, relatively simple to manufacture, and comparatively cost effective.
The present invention is directed to a plasma mass filter for separating low-mass to charge particles from high-mass to charge particles in a multi-species plasma. For the present invention, the filter includes a substantially cylindrically shaped barrier having a first end and a second end. The barrier is formed with an inner wall and an outer wall, with the inner wall surrounding a chamber and defining a longitudinal axis.
Preferably, four helically shaped coils are mounted on the outer wall to establish a magnetic field in the chamber. Specifically, each helical coil is formed in the shape of a helix to wrap around the outside of the barrier and extend from the first end of the barrier to the second end of the barrier. Further, the four helical coils have a common angle of inclination and preferably are evenly spaced around the circumference of the barrier. Stated another way, at the first end, second end and on every cross section normal to the axis, the four helical coils are equally spaced (i.e. spaced approximately 90 degrees apart).
For the present invention, a current is passed through the helically shaped coils to establish a magnetic field within the chamber. Preferably, the current in two of the helically shaped coils travels in a direction from the first end to the second end while the current in the other two helically shaped coils travels in a direction from the second end to the first end. Specifically, each pair of opposed coils (i.e. coils that are spaced 180 degrees at the ends of the barrier) have currents flowing in the same direction.
In addition to the helically shaped coils, an optional set of coils is provided to superimpose an axial magnetic field having strength, B0, with the field from the helical coils. For this purpose, the optional coils may take the form of annular shaped coils mounted to the outer wall of the barrier. With this combination of structure, a magnetic field can be established inside the chamber having components:
xe2x80x83Br=xe2x88x92ibImxe2x80x2[kr]exp[imxcex8+ikz]
Bxcex8=[b/kr]Imexp[imxcex8+ikz]
Bz=bImexp[imxcex8+ikz]+B0
at each location with coordinates {r, xcex8, z} in the chamber. For the calculation of these magnetic field components, the point having cylindrical coordinates {r, xcex8, z} equal to {0,0,0} is located on the longitudinal axis, Im is the modified Bessel function, Imxe2x80x2 is the derivative of the modified Bessel function, b is the strength of the helical field and B0 is the uniform axial magnetic field.
For the present invention, the filter further includes a series of conducting rings concentrically centered on the longitudinal axis and positioned at one end of the chamber. When activated, these rings generate an electric field in the chamber that is oriented substantially in a radial direction between the longitudinal axis and the barrier. Preferably, the rings establish a field in the chamber having a positive potential along the longitudinal axis and a substantially zero potential on the inner wall of the barrier.
In the operation of the present invention, the magnitude of the magnetic field components Br, Bxcex8, Bz, and the magnitude of the positive potential, xe2x80x9cVctrxe2x80x9d, along the longitudinal axis of the chamber are set. Next, a multi-species plasma having both low-mass and high-mass particles is injected into the chamber at the first end of the barrier for interaction with the electric and magnetic fields. In accordance with the mathematics outlined above, for the B0 greater than b cutoff mass, Mc, between high-mass and low-mass particles is given by the expression:
Mc=e(B0(B0xe2x88x92b))R2/8Vctr
where e is the magnitude of the electron charge, and R is the radius of the wall.
Inside the chamber, the electric and magnetic fields combine to place the high-mass particles (i.e. particles having mass greater than Mc) onto trajectories rotating about a guiding center that travels on a surface having a hyperbolic shape. As such, these high-mass particles are ejected from the chamber for collection at the inner wall of the barrier. To the contrary, the electric and magnetic fields combine to place the low-mass particles (i.e. particles having mass less than Mc) onto trajectories rotating about a guiding center that travels on a surface having an elliptical shape. As such, these low-mass particles are confined to a finite volume, and accordingly, transit through the chamber, exiting the chamber at the second end of the barrier.